YES Input TRS: 1: 0(1(2(2(x1)))) -> 0(1(0(2(2(x1))))) 2: 0(1(2(2(x1)))) -> 0(1(2(3(2(x1))))) 3: 0(1(2(2(x1)))) -> 0(2(2(1(3(x1))))) 4: 0(1(2(2(x1)))) -> 1(0(3(2(2(x1))))) 5: 0(1(2(2(x1)))) -> 1(2(0(3(2(x1))))) 6: 0(1(2(2(x1)))) -> 1(3(0(2(2(x1))))) 7: 0(1(2(2(x1)))) -> 1(3(2(0(2(x1))))) 8: 0(1(2(2(x1)))) -> 0(1(0(4(2(2(x1)))))) 9: 0(1(2(2(x1)))) -> 0(2(1(3(2(3(x1)))))) 10: 0(1(2(2(x1)))) -> 1(2(1(0(4(2(x1)))))) 11: 0(1(2(2(x1)))) -> 1(5(0(4(2(2(x1)))))) 12: 0(1(2(2(x1)))) -> 2(0(3(1(3(2(x1)))))) 13: 0(1(2(2(x1)))) -> 2(1(1(0(4(2(x1)))))) 14: 0(1(2(2(x1)))) -> 2(1(3(0(2(0(x1)))))) 15: 0(1(2(2(x1)))) -> 2(1(3(3(2(0(x1)))))) 16: 0(1(2(2(x1)))) -> 2(1(5(3(0(2(x1)))))) 17: 0(1(2(2(x1)))) -> 2(2(1(3(0(5(x1)))))) 18: 0(1(2(2(x1)))) -> 2(4(1(3(2(0(x1)))))) 19: 0(1(4(5(x1)))) -> 1(5(0(4(1(x1))))) 20: 0(1(4(5(x1)))) -> 5(0(4(1(5(x1))))) 21: 0(1(4(5(x1)))) -> 5(4(1(5(0(x1))))) 22: 0(1(4(5(x1)))) -> 1(1(5(0(4(1(x1)))))) 23: 0(1(4(5(x1)))) -> 5(4(1(5(5(0(x1)))))) 24: 5(1(2(2(x1)))) -> 1(0(2(2(5(x1))))) 25: 5(1(2(2(x1)))) -> 1(3(5(2(2(x1))))) 26: 5(1(2(2(x1)))) -> 1(5(2(3(2(x1))))) 27: 5(1(2(2(x1)))) -> 1(5(0(2(2(3(x1)))))) 28: 5(1(2(2(x1)))) -> 2(1(0(3(2(5(x1)))))) 29: 5(1(2(2(x1)))) -> 3(1(3(5(2(2(x1)))))) 30: 5(1(2(2(x1)))) -> 4(1(3(2(2(5(x1)))))) 31: 5(1(2(2(x1)))) -> 5(1(0(4(2(2(x1)))))) 32: 5(1(2(2(x1)))) -> 5(1(2(0(4(2(x1)))))) 33: 0(1(1(4(5(x1))))) -> 3(1(0(4(1(5(x1)))))) 34: 0(1(2(2(2(x1))))) -> 1(0(2(2(5(2(x1)))))) 35: 0(1(2(2(5(x1))))) -> 1(5(0(4(2(2(x1)))))) 36: 0(1(2(4(5(x1))))) -> 2(5(1(0(4(5(x1)))))) 37: 0(1(4(5(2(x1))))) -> 1(0(4(2(0(5(x1)))))) 38: 0(1(4(5(5(x1))))) -> 5(0(4(0(1(5(x1)))))) 39: 0(1(5(4(5(x1))))) -> 1(5(0(4(1(5(x1)))))) 40: 0(5(1(2(2(x1))))) -> 0(1(3(2(5(2(x1)))))) 41: 3(3(1(2(2(x1))))) -> 1(3(2(0(3(2(x1)))))) 42: 3(4(4(0(5(x1))))) -> 3(5(4(5(0(4(x1)))))) 43: 5(0(1(2(2(x1))))) -> 1(3(2(0(5(2(x1)))))) 44: 5(1(2(2(5(x1))))) -> 1(5(2(3(2(5(x1)))))) 45: 5(2(1(2(2(x1))))) -> 2(1(3(5(2(2(x1)))))) 46: 5(2(4(0(5(x1))))) -> 0(4(2(5(5(5(x1)))))) 47: 5(2(4(0(5(x1))))) -> 0(4(5(4(2(5(x1)))))) Number of strict rules: 47 Direct POLO(bPol) ... failed. Uncurrying 3 1: 0(1(2(2(x1)))) -> 0(1(0(2(2(x1))))) 2: 0(1(2(2(x1)))) -> 0(1(2(3^1_2(x1)))) 3: 0(1(2(2(x1)))) -> 0(2(2(1(3(x1))))) 4: 0(1(2(2(x1)))) -> 1(0(3^1_2(2(x1)))) 5: 0(1(2(2(x1)))) -> 1(2(0(3^1_2(x1)))) 6: 0(1(2(2(x1)))) -> 1(3(0(2(2(x1))))) 7: 0(1(2(2(x1)))) -> 1(3^1_2(0(2(x1)))) 8: 0(1(2(2(x1)))) -> 0(1(0(4(2(2(x1)))))) 9: 0(1(2(2(x1)))) -> 0(2(1(3^1_2(3(x1))))) 10: 0(1(2(2(x1)))) -> 1(2(1(0(4(2(x1)))))) 11: 0(1(2(2(x1)))) -> 1(5(0(4(2(2(x1)))))) 12: 0(1(2(2(x1)))) -> 2(0(3^1_1(3^1_2(x1)))) 13: 0(1(2(2(x1)))) -> 2(1(1(0(4(2(x1)))))) 14: 0(1(2(2(x1)))) -> 2(1(3(0(2(0(x1)))))) 15: 0(1(2(2(x1)))) -> 2(1(3^2_2(0(x1)))) 16: 0(1(2(2(x1)))) -> 2(1(5(3(0(2(x1)))))) 17: 0(1(2(2(x1)))) -> 2(2(1(3(0(5(x1)))))) 18: 0(1(2(2(x1)))) -> 2(4(1(3^1_2(0(x1))))) 19: 0(1(4(5(x1)))) -> 1(5(0(4(1(x1))))) 20: 0(1(4(5(x1)))) -> 5(0(4(1(5(x1))))) 21: 0(1(4(5(x1)))) -> 5(4(1(5(0(x1))))) 22: 0(1(4(5(x1)))) -> 1(1(5(0(4(1(x1)))))) 23: 0(1(4(5(x1)))) -> 5(4(1(5(5(0(x1)))))) 24: 5(1(2(2(x1)))) -> 1(0(2(2(5(x1))))) 25: 5(1(2(2(x1)))) -> 1(3(5(2(2(x1))))) 26: 5(1(2(2(x1)))) -> 1(5(2(3^1_2(x1)))) 27: 5(1(2(2(x1)))) -> 1(5(0(2(2(3(x1)))))) 28: 5(1(2(2(x1)))) -> 2(1(0(3^1_2(5(x1))))) 29: 5(1(2(2(x1)))) -> 3^1_1(3(5(2(2(x1))))) 30: 5(1(2(2(x1)))) -> 4(1(3^1_2(2(5(x1))))) 31: 5(1(2(2(x1)))) -> 5(1(0(4(2(2(x1)))))) 32: 5(1(2(2(x1)))) -> 5(1(2(0(4(2(x1)))))) 33: 0(1(1(4(5(x1))))) -> 3^1_1(0(4(1(5(x1))))) 34: 0(1(2(2(2(x1))))) -> 1(0(2(2(5(2(x1)))))) 35: 0(1(2(2(5(x1))))) -> 1(5(0(4(2(2(x1)))))) 36: 0(1(2(4(5(x1))))) -> 2(5(1(0(4(5(x1)))))) 37: 0(1(4(5(2(x1))))) -> 1(0(4(2(0(5(x1)))))) 38: 0(1(4(5(5(x1))))) -> 5(0(4(0(1(5(x1)))))) 39: 0(1(5(4(5(x1))))) -> 1(5(0(4(1(5(x1)))))) 40: 0(5(1(2(2(x1))))) -> 0(1(3^1_2(5(2(x1))))) 41: 3^2_1(2(2(x1))) -> 1(3^1_2(0(3^1_2(x1)))) 42: 3^1_4(4(0(5(x1)))) -> 3(5(4(5(0(4(x1)))))) 43: 5(0(1(2(2(x1))))) -> 1(3^1_2(0(5(2(x1))))) 44: 5(1(2(2(5(x1))))) -> 1(5(2(3^1_2(5(x1))))) 45: 5(2(1(2(2(x1))))) -> 2(1(3(5(2(2(x1)))))) 46: 5(2(4(0(5(x1))))) -> 0(4(2(5(5(5(x1)))))) 47: 5(2(4(0(5(x1))))) -> 0(4(5(4(2(5(x1)))))) 48: 3(2(_1)) ->= 3^1_2(_1) 49: 3(3^1_2(_1)) ->= 3^2_2(_1) 50: 3(1(_1)) ->= 3^1_1(_1) 51: 3(3^1_1(_1)) ->= 3^2_1(_1) 52: 3(4(_1)) ->= 3^1_4(_1) Number of strict rules: 47 Direct POLO(bPol) ... removes: 18 4 15 26 28 44 5 7 49 30 12 9 40 48 41 43 2 1 w: x1 4 w: x1 5 w: x1 3 w: x1 3^1_4 w: x1 0 w: x1 2 w: x1 + 35859 3^1_1 w: x1 3^1_2 w: x1 + 35858 3^2_2 w: x1 + 32755 3^2_1 w: x1 Number of strict rules: 32 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #5(1(2(2(x1)))) -> #3(5(2(2(x1)))) #2: #5(1(2(2(x1)))) -> #5(2(2(x1))) #3: #0(1(2(2(5(x1))))) -> #5(0(4(2(2(x1))))) #4: #0(1(2(2(5(x1))))) -> #0(4(2(2(x1)))) #5: #5(2(4(0(5(x1))))) -> #0(4(2(5(5(5(x1)))))) #6: #5(2(4(0(5(x1))))) -> #5(5(5(x1))) #7: #5(2(4(0(5(x1))))) -> #5(5(x1)) #8: #3^1_4(4(0(5(x1)))) -> #3(5(4(5(0(4(x1)))))) #9: #3^1_4(4(0(5(x1)))) -> #5(4(5(0(4(x1))))) #10: #3^1_4(4(0(5(x1)))) -> #5(0(4(x1))) #11: #3^1_4(4(0(5(x1)))) -> #0(4(x1)) #12: #0(1(4(5(2(x1))))) -> #0(4(2(0(5(x1))))) #13: #0(1(4(5(2(x1))))) -> #0(5(x1)) #14: #0(1(4(5(2(x1))))) -> #5(x1) #15: #5(2(4(0(5(x1))))) -> #0(4(5(4(2(5(x1)))))) #16: #5(2(4(0(5(x1))))) -> #5(4(2(5(x1)))) #17: #0(1(4(5(5(x1))))) -> #5(0(4(0(1(5(x1)))))) #18: #0(1(4(5(5(x1))))) -> #0(4(0(1(5(x1))))) #19: #0(1(4(5(5(x1))))) -> #0(1(5(x1))) #20: #0(1(2(2(x1)))) -> #3(0(2(2(x1)))) #21: #0(1(2(2(x1)))) -> #0(2(2(x1))) #22: #0(1(2(2(x1)))) -> #0(4(2(x1))) #23: #0(1(2(2(x1)))) -> #5(0(4(2(2(x1))))) #24: #0(1(2(2(x1)))) -> #0(4(2(2(x1)))) #25: #5(1(2(2(x1)))) -> #0(2(2(5(x1)))) #26: #5(1(2(2(x1)))) -> #5(x1) #27: #0(1(4(5(x1)))) -> #5(4(1(5(5(0(x1)))))) #28: #0(1(4(5(x1)))) -> #5(5(0(x1))) #29: #0(1(4(5(x1)))) -> #5(0(x1)) #30: #0(1(4(5(x1)))) -> #0(x1) #31: #5(2(1(2(2(x1))))) -> #3(5(2(2(x1)))) #32: #5(2(1(2(2(x1))))) -> #5(2(2(x1))) #33: #5(1(2(2(x1)))) -> #5(1(0(4(2(2(x1)))))) #34: #5(1(2(2(x1)))) -> #0(4(2(2(x1)))) #35: #0(1(2(2(x1)))) -> #3(0(2(0(x1)))) #36: #0(1(2(2(x1)))) -> #0(2(0(x1))) #37: #0(1(2(2(x1)))) -> #0(x1) #38: #3(4(_1)) ->? #3^1_4(_1) #39: #5(1(2(2(x1)))) -> #3(5(2(2(x1)))) #40: #5(1(2(2(x1)))) -> #5(2(2(x1))) #41: #0(1(4(5(x1)))) -> #5(0(4(1(5(x1))))) #42: #0(1(4(5(x1)))) -> #0(4(1(5(x1)))) #43: #0(1(5(4(5(x1))))) -> #5(0(4(1(5(x1))))) #44: #0(1(5(4(5(x1))))) -> #0(4(1(5(x1)))) #45: #0(1(2(2(x1)))) -> #0(4(2(x1))) #46: #0(1(1(4(5(x1))))) -> #0(4(1(5(x1)))) #47: #0(1(4(5(x1)))) -> #5(0(4(1(x1)))) #48: #0(1(4(5(x1)))) -> #0(4(1(x1))) #49: #0(1(2(2(2(x1))))) -> #0(2(2(5(2(x1))))) #50: #0(1(2(2(2(x1))))) -> #5(2(x1)) #51: #5(1(2(2(x1)))) -> #5(0(2(2(3(x1))))) #52: #5(1(2(2(x1)))) -> #0(2(2(3(x1)))) #53: #5(1(2(2(x1)))) -> #3(x1) #54: #0(1(2(2(x1)))) -> #3(0(5(x1))) #55: #0(1(2(2(x1)))) -> #0(5(x1)) #56: #0(1(2(2(x1)))) -> #5(x1) #57: #0(1(4(5(x1)))) -> #5(0(4(1(x1)))) #58: #0(1(4(5(x1)))) -> #0(4(1(x1))) #59: #5(1(2(2(x1)))) -> #5(1(2(0(4(2(x1)))))) #60: #5(1(2(2(x1)))) -> #0(4(2(x1))) #61: #0(1(2(4(5(x1))))) -> #5(1(0(4(5(x1))))) #62: #0(1(2(4(5(x1))))) -> #0(4(5(x1))) #63: #0(1(4(5(x1)))) -> #5(4(1(5(0(x1))))) #64: #0(1(4(5(x1)))) -> #5(0(x1)) #65: #0(1(4(5(x1)))) -> #0(x1) #66: #0(1(2(2(x1)))) -> #5(3(0(2(x1)))) #67: #0(1(2(2(x1)))) -> #3(0(2(x1))) #68: #0(1(2(2(x1)))) -> #0(2(x1)) #69: #0(1(2(2(x1)))) -> #0(2(2(1(3(x1))))) #70: #0(1(2(2(x1)))) -> #3(x1) #71: #0(1(2(2(x1)))) -> #0(1(0(2(2(x1))))) #72: #0(1(2(2(x1)))) -> #0(2(2(x1))) #73: #0(1(2(2(x1)))) -> #0(1(0(4(2(2(x1)))))) #74: #0(1(2(2(x1)))) -> #0(4(2(2(x1)))) Number of SCCs: 2, DPs: 4 SCC { #26 } POLO(Sum)... succeeded. #0 w: 0 1 w: x1 4 w: 0 5 w: 0 3 w: 0 3^1_4 w: 0 0 w: 0 #3 w: 0 #5 w: x1 2 w: x1 + 1 3^1_1 w: 0 3^1_2 w: 0 3^2_2 w: 0 #3^1_4 w: 0 3^2_1 w: 0 USABLE RULES: { } Removed DPs: #26 Number of SCCs: 1, DPs: 3 SCC { #30 #37 #65 } POLO(Sum)... succeeded. #0 w: x1 1 w: x1 4 w: x1 5 w: x1 + 1 3 w: 0 3^1_4 w: 0 0 w: 0 #3 w: 0 #5 w: 0 2 w: x1 + 20653 3^1_1 w: 0 3^1_2 w: 0 3^2_2 w: 0 #3^1_4 w: 0 3^2_1 w: 0 USABLE RULES: { } Removed DPs: #30 #37 #65 Number of SCCs: 0, DPs: 0